Precisely move the 3D cursor
An updated 2.8 answer can be found here

In both edit mode and object mode; press N to open the Properties. Scroll down to the 3D cursor. There are three number fields one each for the X, Y, and Z axes.
For finer control use Alt or Ctrl while dragging the mouse. Also see the Manual.

Note the coordinates are always in Global, how the transform orientation is set makes no difference.